Organic π-conjugated materials exhibit exceptional nonlinear optical (NLO) properties due to their unique electronic structures, characterized by short response times and large NLO responses. Fullerene (C60) is one of the few polymer species that possess a rich π-conjugated system, making it a promising material with significant NLO responses. In the present paper, we designed three C60 polymer fragments and employed density functional theory to estimate their molecular static first and second hyperpolarizabilities. Compared to previously reported fullerene derivatives, the designed C60 polymer fragments can exhibit notable second-order and third-order molecular NLO responses. The study shows that the hyperpolarizabilities and energy gaps of the investigated C60 polymer fragments are greatly influenced by their topological structures and bonding modes. These findings provide new insights for the design of novel NLO materials based on C60 polymers, and the realization of tunable NLO responses in C60 cluster-based molecular systems, which may have significant applications in nanophotonic devices.